Functional Data Analysis (FDA)

High-performance Functional Data Analysis tools implemented in Rust with R bindings.

Packages

Package	Language	Registry	Folder	Status
fdars	R	CRAN	sipemu/fdars-r
fdars-core	Rust	crates.io	`fdars-core/`

Features

Area	Capabilities
Core	Simulation (KL expansion, GP with 8 kernels), functional operations, smoothing (NW, local polynomial, k-NN), basis representations (B-spline, Fourier, P-spline)
Descriptive	10 depth measures + streaming online depth, 12 distance metrics (Lp, DTW, elastic, semimetrics, KL), LRT outlier detection
Regression	Scalar-on-function (FPC, kernel, logistic, robust), function-on-scalar (FOSR, 2D FOSR, FANOVA), FPCA, PLS, ridge, mixed effects
Classification	LDA, QDA, k-NN, kernel, DD-classifier, conformal prediction sets; k-means, fuzzy c-means, GMM
Elastic Alignment	SRSF/DP alignment, Karcher mean (1-D/N-D), TSRVF, Bayesian (pCN MCMC), closed curves, transfer alignment, partial matching, multi-resolution, generative models, geodesics, FPNS, lambda CV, peak persistence
Elastic Robust	Karcher median, trimmed mean, SRVF outlier detection, elastic depth, shape CIs, diagnostics, warp statistics, phase box plots, shape analysis
Elastic Models	Elastic FPCA, regression, PCR, logistic, scalar-on-shape (ScoSh), changepoint detection, elastic clustering
SPM	T²/SPE Phase I/II, EWMA, MEWMA, CUSUM, adaptive EWMA, FRCC, profile monitoring; bootstrap/KDE limits, ARL, partial-domain, elastic SPM, iterative Phase I, Western Electric/Nelson rules
Explainability	PDP/ICE, SHAP, ALE, LIME, Sobol, Friedman H, anchors, counterfactuals, prototype/criticism; influence diagnostics, VIF, calibration (ECE, Brier), saliency maps; `FpcPredictor` trait
Inference	Tolerance bands (FPCA, conformal, Degras, exponential, elastic), conformal prediction (split, Jackknife+, CV+), equivalence testing (TOST)
Time Series	Seasonal detection (FFT, ACF, Autoperiod, SAZED, Lomb-Scargle, SSA, matrix profile), detrending (polynomial, LOESS, STL)
Specialized	Streaming depth (online O(log N)), irregular data (CSR, kernel estimation)

Installation

R (fdars)

install.packages("fdars")

# Development version from GitHub (requires Rust toolchain)
devtools::install_github("sipemu/fdars-r")

Rust (fdars-core)

[dependencies]
fdars-core = "0.9"

Or install from the repository:

[dependencies]
fdars-core = { git = "https://github.com/sipemu/fdars" }

Feature Flags

parallel (default): Enable rayon-based parallel processing
linalg: Enable linear algebra features (faer, ridge regression) — requires Rust 1.84+
js: Enable WASM support with JS random number generation

For WASM builds, disable default features:

[dependencies]
fdars-core = { version = "0.9", default-features = false }

Data Layout

Functional data is represented using the FdMatrix type, a column-major matrix wrapping a flat Vec<f64> with safe (i, j) indexing and dimension tracking:

For n observations with m evaluation points: data[(i, j)] gives observation i at point j
Zero-copy column access via data.column(j), row gather via data.row(i)
nalgebra interop via to_dmatrix() / from_dmatrix() for SVD operations
2D surfaces (n observations, m1 x m2 grid): stored as n x (m1*m2) matrices

Quick Start

use fdars_core::{FdMatrix, fdata, depth};

// Create sample functional data (3 observations, 10 points each)
let n = 3;
let m = 10;
let data: Vec<f64> = (0..(n * m)).map(|i| (i as f64).sin()).collect();
let mat = FdMatrix::from_column_major(data, n, m).unwrap();
let argvals: Vec<f64> = (0..m).map(|i| i as f64 / (m - 1) as f64).collect();

// Compute mean function
let mean = fdata::mean_1d(&mat);

// Compute Fraiman-Muniz depth
let depths = depth::fraiman_muniz_1d(&mat, &mat, true);

Examples

27 runnable examples in fdars-core/examples/:

#	Example	Topics
01	Simulation	KL expansion, GP generation
02	Functional Operations	Mean, derivatives, norms
03	Smoothing	NW, local polynomial, k-NN
04	Basis Representation	B-splines, Fourier, P-splines
05	Depth Measures	8 depth measures, outlier ranking
06	Distances	Lp, DTW, elastic, semimetrics
07	Clustering	K-means, fuzzy c-means
08	Regression	FPCA, PLS
09	Outlier Detection	LRT bootstrap
10	Seasonal Analysis	FFT, Autoperiod, SAZED
11	Detrending	Polynomial, LOESS, STL
12	Streaming Depth	Online depth
13	Irregular Data	CSR storage, kernel estimation
14	Complete Pipeline	End-to-end workflow
15	Tolerance Bands	FPCA, conformal, Degras SCB
16	Elastic Alignment	SRSF, DP, Karcher mean
17	Equivalence Test	Functional TOST
18	Landmark Registration	Constrained alignment
19	TSRVF	Transported SRVF
20	Scalar-on-Function `*`	FPC linear, logistic, kernel
21	Function-on-Scalar `*`	FOSR, FANOVA
22	GMM Clustering `*`	GMM-EM, BIC/ICL
23	Classification `*`	LDA, QDA, k-NN, DD
24	Mixed Effects `*`	FAMM, REML
25	Explainability `*`	SHAP, ALE, PDP, anchors
26	Elastic Analysis `*`	Elastic FPCA, regression, PCR
27	SPM	Phase I/II, EWMA, CUSUM, rules

* requires --features linalg

Run with cargo run -p fdars-core --example <name> (add --features linalg where marked).

Performance

With the parallel feature (enabled by default), computationally intensive operations use rayon for multi-core performance. The library also supports WASM targets with sequential execution.

Documentation

R Package: https://sipemu.github.io/fdars/
Rust Crate: https://docs.rs/fdars-core

License

MIT